Til I) OUHIT OF URANUS. 5 



but witliout any dt tails v/liatcvor of tin- investigation, or any statement of the 

 method* cni[>lM\t (!. 'Hit- miniitnie.vs of the residuals in the last column of the 

 preceding table slums that employing these perturbations by Neptune, and those 

 of Le Verrier by Jupiter and Saturn, we had a theory of Uranus from which quite 

 accurate tables might have been constructed. But this never seems to have been 

 done. The ephemeris of Uranus in the American Nautical Almanac was intended 

 to be founded on this theory, but the proper definitive elements do not seem to 

 have been adopted iii the computations, as the ephemeris does not correspond with 

 the theory. 



Although twenty-ti\e \ears have elapsed since the epoch of these researches, I 

 am not aware of any published work of importance on the theory of Uranus during 

 the interval. Mr. T. II. Safford has, however, made a very extended investigation 

 of the subject, but has published nothing more than a brief general description of 

 his work, which may be found in the Monthly Notices of the Royal Astronomical 

 Sori. ty. Vol. -J-J. Like Professor Peircc, he took Le Verrier's perturbations by 

 Jupiter and Saturn, but, instead of using general perturbations by Neptune, he 

 computed the effect of the action of this planet by mechanical quadratures for the 

 whole period of the observations of Uranus, and thus corrected the elements and 

 the mass of Neptune from modern observations alone. The mass in question 

 deduced was 



1- 



30039 



Mr. Safford does not give the representation of the modern observations, but pre- 

 sents the following comparison of the ancient ones, alongside which we place for 

 comparison the corresponding numbers of Peirce's theory and those of the present 



investigation. 



EXCESS or OBSERVATION OVER THEORY. 



Pelrce. Newoomb. 



0".8 11" 



8.T 8 



'} +2.9 



4.0 



+ 6.0 1.4 



